In each problem 7 through 14, verify that each given function is a solution of the differential equation. Y" - y = 0; y1(t) = et, y2(t) = cosh t.

Answers

Answer 1

Answer:

Since L.H.S = R.H.S = 0, for both [tex]y_{1} (t) = e^{t}[/tex] and [tex]y_{2} (t) = cosh(t)[/tex], y₁ and y₂ both satisfy the equation y" - y = 0 and are thus solutions to the differential equation.

Step-by-step explanation:

To check whether the given functions are solutions the given differential equation, we differentiate the functions and then insert it into the given equation.

So y" - y = 0 and  

[tex]y_{1} (t) = e^{t}\\y_{1}' (t) = e^{t}\\ y_{1}" (t) = e^{t}[/tex]

Substituting these values of y and y" into the left hand side of the equation, we have

y" - y  

[tex]y_{1}" (t) - y_{1} (t) = e^{t} - e^{t} = 0[/tex]

Since L.H.S = R.H.S

So [tex]y_{1} (t) = e^{t}[/tex] is a solution of the differential equation.

When

[tex]y_{2} (t) = cosh(t)\\ y_{2}'(t) = sinh(t) \\y_{2}"(t) = cosh(t)[/tex]

Substituting y and y" into the left hand side of the equation, we have

y" - y

[tex]y_{2}"(t) - y_{2} (t) = cosh(t) - cosh(t) = 0[/tex]

Since L.H.S = R.H.S

So, [tex]y_{2} (t) = cosh(t)[/tex] is a solution of the differential equation.


Related Questions

What is the distance between the points (3,-2) and (-4, 1)?

Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ \sqrt{58} \: \: units}}}}}[/tex]

Step-by-step explanation:

Let the points be A and B

Let A ( 3 , -2 ) be ( x₁ , y₁ ) and B ( -4 , 1 ) be ( x₂ , y₂ )

Finding the distance between these points

[tex] \boxed{ \sf{distance = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ {( - 4 - 3)}^{2} + {(1 - ( - 2))}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ {( - 4 - 3)}^{2} + {(1 + 2)}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ {( - 7)}^{2} + {(3)}^{2} } }}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{49 + 9}}} [/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{58} }}[/tex] units

Hope I helped!

Best regards! :D

David and Amrita had an equal number of marbles. After Amrita gave 50 marbles to David, he had 5 times as many marbles as her. Find the total number of marbles they had.

Answers

Answer:

Step-by-step explanation:

a = d before Anna gives away 50 marbles.

 

5 (a-50) = a +50 after Anna gives away 50 marbles.

 

5a - 250 = a + 50

 

4a = 300

 

a = 75

 

Anna has 75 marbles at the beginning and so did David.

 

Together they have 150 marbles.

:)

Answer:

150

Step-by-step explanation:

Originally, they had the same number, so they both had x marbles each.

David: x

Amrita: x

Amrita gives 50 marbles to David. Now they have:

David: x + 50

Amrita: x - 50

"he had 5 times as many marbles as her"

x + 50 = 5(x - 50)

x + 50 = 5x - 250

-4x = -300

x = 75

Each had 75 marbles to start with.

75 + 75 = 150

The total is 150.

Which type of cell contains Cell Membrane?

Answers

Answer:

Eukaryotic cells contain cell membrane!

how do i estimate .48

Answers

To estimate, we can round to the nearest tenth.

How to round:

5 and above, round up.

4 and below, round down.

0.48 -> 0.5

Best of Luck!

What is the solution to this equation?
6x = 36
O A. x = 30
O B. x = 216
C. x = 6
O D. x= 4

Answers

C X=6


36\6= 6 that is why.

Answer:

C

Step-by-step explanation:

6x=36

6x/6 cross out

36/6=6

×=6

so the answer is C

What is represented by the number below the abbreviation of the element in the periodic table? The atomic mass The atomic number The melting point The valence number​

Answers

Answer:

Atomic Mass

Step-by-step explanation:

Correct answer as per the test

The abbreviation of the element in the periodic table will be atomic number. Then the correct option is B.

What is a periodic table?

An arrangement of atoms by their atomic numbers, often in rows, such that atoms with comparable atomic structures (and thus comparable chemical characteristics) are shown in vertical slats.

The abbreviation of the element in the periodic table will be atomic number.

Then the correct option is B.

More about the periodic table link is given below.

https://brainly.com/question/11155928

#SPJ2

A car drives with an average velocity of 20.1 m/s . After some time, it has traveled 34.2 km. How long has the car been traveling?

Answers

Answer:

time = distance / velocity

time = 34,200 meters / 20.1 meters per second

time = 1,701.4925373134 seconds

time = 28.36 minutes

 

Step-by-step explanation:

this is rlly easy but im lazy and dont wana answer it, i mark brainliesttttt tyyy ❤️

Answers

Answer:

C and D is correct

Step-by-step explanation:

C: Debit is negative, and if you add 27 to -14, you get 13 which is Maria's account.

D: Its the same thing but opposite. 13 minus 27 is -14.

Hope it helps

Answer:

both c and d

Step-by-step explanatioin

nobody is answering my question so im saving up like 100 points so someone will actually do it so ye




Plot the point then draw the shape
they create. What shape does it
create?
(2,5)
(7, 1)
(5,5-)
(-1,-5)
(-3,1)

Answers

I drew a graph and plotted the coordinates. a hexagon is the shape u will get

Divide: 21 and 4,291,678

Answers

Answer: assuming you mean divide 4mil by 21, the answer is 204365.619

Step-by-step explanation:

Answer:

4.9x10⁻⁶

Step-by-step explanation:

21 / 4291678 = 4.9x10⁻⁶

Find the area and perimeter of a court with dimensions of 50ft by 84ft.

Answers

Answer:

Area: 4200

Perimeter: 268

Step-by-step explanation:

To find the area, multiply length and width (50 x 84)

To find perimeter, add up the lengths of all the sides (50+50+84+84)

Hope this helps!

Guess and win math cash 0 and 99999

Answers

Answer:

12345

Step-by-step explanation:

乁[ ◕ ᴥ ◕ ]ㄏฅ^•ﻌ•^ฅ▼・ᴥ・▼

0-99999

(IT COULd Be aNy?) This writing was a joke. BUT WHAT IS THE ANSWER!!!!!!!!

Find the population mean or sample mean as indicated.Sample: 19, 15, 6, 11, 24Required:Compute the sample mean for this data set.

Answers

Answer:

The sample mean is 15.

Step-by-step explanation:

We have given data 19, 15, 6, 11, 24.

We are required to find the sample mean. The sample mean can be determined by adding all the given value and then divide by the total numbers or how many numbers. Below is the calculation of the mean.

Sample mean = (19+ 15 +6 +11 +24) / 5

Sample mean = 75 / 5

Sample mean = 15

Therefore the sample mean of the given data is 15.

15 = x + 13
which property could be used to solve this equation

Answers

Steps to solve:

15 = x + 13

~Subtract 13 to both sides

2 = x

Best of Luck!

Ahmed wrote two numbers the first number has a seven and it’s tenths place the second number has a seven with a value that is 1000 times greater than the value of the seven in the first in which place is a seven and the second number

Answers

Answer: I think the answer is thousands

Step-by-step explanation:

Answer:

100,000

Step-by-step explanation:

first # = 70, 2 digits

second # = 1,000 times greater than 70  1,000 = 4 digits

4 + 2 = 6, 100,000 = 6 digits

driving 85 miles in 5/6 of a hour how many miles per hour

Answers

Hey there! I'm happy to help!

To get 5/6 to 1, you multiply by 6/5. This means that to see your mph, you multiply 85 by 6/5!

85(6/5)=102

The speed is 102 mph.

Have a wonderful day! :D

A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. The actual dimensions of the building are 30 feet long by 55 feet wide. true or false

Answers

1 inch = 10 feet.

3 inches x 10 = 30 feet

5.5 inches x 10 = 55 feet

The actual room is 30 feet x 55 feet.

The answer is true.

Answer:

Round up to the Nernst number

Step-by-step explanation:

45 inches

PLEASE HELP ME I WILL MARK AS BRAINLIEST ANSWER

A map has a scale of
6 in=12 mi. If you measured the distance between two cities to
be 22 in. on the map, how many miles would it actually be?
If necessary, round your answer to the nearest tenth.

Answers

Answer:

The answer is 264

Step-by-step explanation:

We start with a ratio of inches to miles-        6:12

we see that it can be simplified to                  1:2

if we see that on the map it is 22in,             22:?

we got 1 to 22 by multiplying 1*22=22

do the same to the 12: 12*22=264

A randomized study compared two different techniques for improving one's memory. The treatment group using Technique A reported that the subjects were able to memorize a mean of 8.9 words. The treatment group using Technique B reported that the subjects were able to memorize a mean of 12.1 words. To determine if the results are significant, the data are re-randomized and the differences of the means are shown in the dot plot. What is the best conclusion to make based on the data?

Answers

Answer:

The best conclusion that can be made based on the data on the dot plot is:

The mean difference is not significant because the re-randomization show that it is within the range of what could happen by chance.

Step-by-step explanation:

Randomization is the standard used to compare the observational study and balance the factors between the treatment groups and eliminate the variables' influence. Some studies analyze that the treatment in the randomization calculates the appropriate number of the subjects as the treatment to memorize is 8.9, and the treatment for the B is 12.1 words.

The mean difference is not significant because the re-randomization shows that it is within the range of what could happen by chance.

The treatment group using technique A reported a mean of 8.9 words.

The treatment group using technique B reported a mean of 12.1 words.

After the data are re-randomized, the differences of means are shown in the dot plot.

The result is significant because the re-randomization show that it is outside the range. The best conclusion that can be made based on the data on the dot plot is:

The mean difference is not significant because the re-randomization show that it is within the range of what could happen by chance.

Answer:

The answer is actually

-The difference of the means is significant because the re-randomizations show that it is outside the range of what could happen by chance.

*just took the test hope this helps:)*

what is the 3rd square root of 1000

Answers

Answer:

10

Step-by-step explanation:

The third square root is the cube root. This means we are looking for the number that multiplies by itself 3 times to get to 1000, which is 10. (10x10x10=1000)

Hope this helped!

which fraction represents 56 shares evenly distributed among 12 people

Answers

Answer:

14/3

Step-by-step explanation:

When 56 shares are evenly distributed between 12 people, each person gets equal number of shares.

The number of shares gotten by each person is the ratio of the total number of shares to the total number of people. It is given by the formula:

number of shares gotten by each person = total number of shares / total number of people

number of shares gotten by each person = 56 shares / 12 people

number of shares gotten by each person = 14/3 shares

ILL GIVE YOU BRAINLIST !!! HAVE TO GET IT RIGHT !!

Evaluate the expression given the replacement values

Answers

Answer:

8

Step-by-step explanation:

[tex]\frac{2}{5} (1+24) + \frac{1}{2} (2-6)[/tex]=

[tex]\frac{2}{5} (25)+ \frac{1}{2} (-4)[/tex]=

[tex]10-2=8[/tex]

ILL GIVE YOU BRAINLIST !!! HAVE TO GET IT RIGHT !!

Evaluate the expression given the replacement values

Answers

Answer:

207

Step-by-step explanation:

[tex]w^{2}[/tex]=9, but since there is a negative sign, it will be negative 9.

-11(uv) is -11(-8), and that equals 88.

2[tex]v^{2}[/tex] is 2(64), which equals 128.

-9+88+128 is 207.

Hope that helps!

Help i dont understand Pls help :( Given g(x)=-4x-2g(x)=−4x−2, find g(-2)g(−2).

Answers

Answer:

[tex]g(-2)=6[/tex]

Step-by-step explanation:

Hi again!

So we have the equation:

[tex]g(x)=-4x-2[/tex]

To find g(-2), substitute -2 for x. Thus:

[tex]g(-2)=-4(-2)-2[/tex]

Multiply. -4 times -2 is positive 8:

[tex]g(-2)=8-2[/tex]

Subtract:

[tex]g(-2)=6[/tex]

And we're done!

a rectangle is 41 cm on one side and 12 cm on the other side.what is the perimeter?

Answers

Answer: 106cm

Explanation: (L+W)2
(41+12)2
82+24=106

Answer:

106

Step-by-step explanation:

4+y when y = 18 would the answer be 22

Answers

Yes you are correct.

You replace y with 18 to get 4+y = 4+18 = 22.


a. Plot 13.58 on a number line on which the long
tick marks are whole numbers.
b. Plot 0.193 on a number line on which the long
tick marks are tenths.
c. Plot 26.9999 on a number line on which the
long tick marks are thousandths.

Answers

Answer:

Se attached for plots and here is position of the numbers:

a. Plot 13.58 on a number line on which the long

tick marks are whole numbers.

13 < 13.58 < 14

b. Plot 0.193 on a number line on which the long

tick marks are tenths.

0.1 < 0.193 < 0.2

c. Plot 26.9999 on a number line on which the

long tick marks are thousandths.

26.999 < 26.9999 < 27.000

Find the point (x1,x2) that lies on the line x1 +5x2 =7 and on the line x1 - 2x2 = -2.

Answers

Given :

Two equation [tex]x_1 +5x_2 =7[/tex] and [tex]x_1 - 2x_2 = -2[/tex] .

To Find :

The point of intersection of these lines .

Solution :

We will use elimination method :

From equation 1 :

[tex]x_1=7-5x_2[/tex]

Putting value of [tex]x_1[/tex] in equation 2 we get :

[tex](7-5x_2)-2x_2=-2\\\\7-7x_2=-2\\\\x_2=\dfrac{9}{7}[/tex]

Putting value of [tex]x_2[/tex] in equation 1 we get :

[tex]x_1+5\times \dfrac{9}{7}=7\\\\x_1=\dfrac{4}{7}[/tex]

Therefore , point of interaction is [tex](\dfrac{4}{7},\dfrac{9}{7})[/tex] .

Hence , this is the required solution .

The point is: [tex]\left(x_{1},x_{2}\right)=\left(\frac{4}{7},\frac{9}{7}\right)[/tex]

We will solve the given system of equations.

Subtract the second equation from the first one:

[tex]\left(x_{1}+5x_{2}\right)-\left(x_{1}-2x_{2}\right)=7-\left(-2\right)\\x_{1}+5x_{2}-x_{1}+2x_{2}=7+2\\7x_{2}=9\\x_{2}=\frac{9}{7}[/tex]

Then we plug [tex]x_{2}=\frac{9}{7}[/tex] in the given first equation.

[tex]x_{1}+5x_{2}=7\\x_{1}+5\left(\frac{9}{7}\right)=7\\x_{1}+\frac{45}{7}=7\\x_{1}=7-\frac{45}{7}\\x_{1}=\frac{4}{7}[/tex]

So the point is: [tex]\left(x_{1},x_{2}\right)=\left(\frac{4}{7},\frac{9}{7}\right)[/tex]

Learn more: https://brainly.com/question/16236436

The temperature in a town is 24.8 during the day and -8.1 at night. Find the difference in the temperatures.

Answers

The difference is exactly 32.9 degrees

63x^12-35x^6 help pls

Answers

Answer:

7x^6×(9×^6-5)

Step-by-step explanation:

63x^12-35x^6

7x^6×(9×^6-5)

Answer:I dont know

Step-by-step explanation: Can you pls rate this good I am in 2 grade

Other Questions
Find the solution for the following: Three backpackers cooked rice for dinner. The first one gave 400g of rice and the second 200g of rice. The third one did not have any rice so he gave $6 to the other two. How should they divide the $6 in a fair way ( assume they equally shared the dinner) ? Daniel growing corn in a square field. The length of one side is 100 yards he needs to purchase fertilizer for the corn field. Each bag covers 50 square yards .How many bags do he need? If you want to replicate another scientist's experiment, which sections of their laboratory report will provide you with the most valuable information? What is 350 divided by 55 as a decimal? A) 6.6 B) 6.36 C) 6.363 D) 6.363 According to the Constitution, how long is a senator's term?two yearsfour yearssix yearseight years x2 + y2 = 13x - y2 = -16Solve When Mr. White states that hed like to go to India, just like Sergeant-Major Morris, Morris tells him better where you are. In what way might this be foreshadowing? 88927+50 is blank than 88927 How do you find the area? You are a manager of a soft drinks company that is planning to go head to head with Coca-Cola to increase market share. Your strategy is to increase your product ranges that you plan to offer to Mass Market. Along with the extension of the products and product lines, you want to be responsive to the different geographic regions you plan to serve. So, your main focus is to balance the extended product categories along with the responsiveness to the geographic regions to serve. Currently you have a functional structure which may not be suitable for maintaining Products along with Geographic Responsiveness. Point Q'Q Q, prime is the image of Q(0,6)Q(0,6)Q, left parenthesis, 0, comma, 6, right parenthesis under the translation (x,y)\to(x+7,y-5)(x,y)(x+7,y5)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 7, comma, y, minus, 5, right parenthesis. What are the coordinates of Q'Q Which is the best definition of point of view in fiction?A. The events that happened before the main actionB. The perspective through which a story is toldC. The main character's vision of people and the worldD. The location in which the story is primarily set Explain why space is such an important concept of art? How did art change following the invention of linear prospective The DNA sequence of a gene for a protein:______.a. mutates at a high rate.b. is a polymer of four ribonucleotides.c. ultimately determines the amino acid sequence of a protein.d. is a nonlinear code. Read the passage below. Lastly, the cookies are arranged in small circles on the cookie sheet and placed into the oven for baking. Where would this sentence appear within a paragraph? the beginning the middle the ending no particular place 1. An arrow is shot with an initial velocity of 60.0 m/s at an angle of 30.0 above the horizontal. What is the maximum height it will reach?a. 23 mb. 46 mc. 69 md. 92 m2. A projectile is launched horizontally from a cliff with an initial speed of 40 m/s. The cliff is 125 m high and the projectile travels a horizontal distance of 200 m from the bottom of the cliff. What is the speed of the projectile right before it hits the ground?a. 48 m/sb. 52 m/sc. 56 m/sd. 60 m/se. 64 m/s 9. This piecewise function represents the Social Security taxes for 2009. How much did Rachel pay in SocialSecurity tax if she earned $102,000 in 2009?(0.062xwhen 0< x < 106,800($6,621.60when x > 106,800Nax)a. $6,824.60b. $6,355.10c. $6,324.00d. $6,220.00 What age does a tree obtain its bark Drag the tiles to the correct boxes to form correct pairs. Not all tiles will be used.Match each example given to the type of scientific concept.theoryhypothesislawobservationIf the amount of daylightincreases plant growth, thenplants will have higher ratesof growth during the summer.arrowBothThe outer layer of the Earth isdivided into plates that movedue to convection currentsunder the surface.arrowBothFor every action or force in nature, there is an equaland opposite reaction.arrowBoth Form a correct sentence by unscrambling the following sentence.duquesa el ve a lal la ve a duquesa.Ve el la a duquesa.l a ve la duquesa.l ve a la duquesa.